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Form a mathematical point of view, one can define ECDSA over arbitrary finite fields. Form a security point of view, the most important thing is the size of the group order. Arithmetic is easy in the case $GF(p)$. Arithmetic gets more involved for $GF(p^m), m>1$, because you have to perform polynomial divisions. Arithmetic in $GF(2^m)$ is ...


The web site of https://ellipter.com says, they are using encryption.


Saying that ECDH does not do authentication is not entirely accurate. If you use ECDH with static, known public keys and both sides prove knowledge of the shared secret, then you do get authentication. However, with ephemeral keys you need some way to authenticate the exchange of public keys. That could be ECDSA or it could be any other authentication. So ...


ECKEY object may contain: Group Private key Public key Both Group and Private key are needed to be able to calculate signature. It is most convenient to use generic ECKEY object (from API perspective), as it easy to e.g. convert between commonly used PKCS#8 PEM encoded EC private keys and ECKEY objects, and because just a BIGNUM would not be sufficient. ...

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